Active RC filter having band-rejection and all-pass modes

ABSTRACT

An active filter circuit operable in a band-rejection mode and in an all-pass mode. A cascade combination of an RC filter and amplifier circuit receives an input signal. A pair of amplifiers respectively receive the input signal and the output of the RC filter and amplifier combination. The outputs of the amplifier pair are summed, and the circuit mode is determined by the RC component values and the amplifier gains.

BACKGROUND OF THE INVENTION

The invention relates to a circuit constituting an active RC filter for band-rejection or all-pass applications in the high frequency and microwave regions.

The invention is used to provide integrated circuits for high-frequency and microwave filters which can, for example, be used in one embodiment as a band-rejection filter in frequency doublers to reject the unwanted signal at the fundamental frequency or, in another embodiment, can be used as an all-pass filter in so far as they are adjustable phase shifters at a given frequency or as all-pass filter in so far as they are elements constituting wide-band 90 degrees phase shifters.

As active all-pass filter is already known from the publication by J. TOW in "IEEE Spectrum, December 1969, pp. 64-68", entitled "A Step-by-step Active-filter Design".

This publication describes, inter alia, a version of an all-pass filter having a biquadratic transfer function, which filter is shown in FIG. 8 of said publication. This circuit comprises three operational amplifiers which are arranged in series, this chain being fed back. A fourth operational amplifier takes the sum of the output of the third operational amplifier and the input of the filter circuit.

The operational amplifiers used to form this circuit have a gain which is certainly infinite for low frequencies, but which becomes very weak for high frequencies and microwaves. For that reason, the circuit disclosed in said document has the disadvantage that it cannot be used in these frequency domains.

On the other hand, the feedback chain has the disadvantages that in certain circumstances it causes the circuit to oscillate.

FIG. 6 of said publication also shows an active band-pass filter which has characteristics which are similar and consequently have the same disadvantage.

The circuits disclosed in said publication have moreover the following drawbacks: on the one hand, they are formed by a large number of transistors, which increases manufacturing cost in all cases to a high level, causes a large surface area to be occupied and is disadvantageous for the use in integrated circuits, and has a high power consumption and is also not suitable for the above application. On the other hand, their characteristic frequency is not adjustable. Finally, the capacitors used in this circuit are of a considerable dimension and are the reason that this circuit is not integrable.

SUMMARY OF THE INVENTION

The present invention proposes an active filter circuit which does not have these drawbacks and which more specifically can operate for high frequency or microwave applications and, in the case they are used for very high frequencies is easily integrable and has a small surface and a low power consumption; and have such characteristics that the frequency characteristic is adjustable.

According to this invention, this object is achieved by means of a circuit characterized in that it comprises a block amplifier A₂ arranged in series with the filter-amplifer block arranged between the output thereof and the output of the circuit. An input signal V_(E) is applied to the adder block via an amplifier A₁, in that the adder block S₃ is formed by coupling the outputs of the amplifier blocks A₁ and A₂ to form the output S of the circuit at which the output signal V_(S) is available.

BRIEF DESCRIPTION OF THE DRAWING

The invention and how it can be put into effect will be better understood from the following description which is given by way of non-limitative example with reference to the accompanying drawings, in which:

FIG. 1 shows the circuit diagram of the circuit according to the invention;

FIG. 2a shows an embodiment of the circuit according to the invention using field-effect transistors;

FIG. 2b shows the equivalent circuit of the passive portion PB of the block F of the circuit of FIG. 2a;

FIGS. 2c and 2d show the curves of the ratio between the output and input voltages of the circuit versus frequency, as regards amplitude and phase, respectively, these curves being obtained by simulation of the circuit shown in FIG. 2a.

DETAILED DESCRIPTION OF THE INVENTION

For a still better understanding of the invention it is pointed out that the transfer function of an active second-order band-rejection filter is given in a Table on pages 94-95 of the book "Filtres Actifs" by Paul BILDSTEIN in "Editions de la Radio" (9 Rue Jacob, Paris, France).

For an ideal second order band-rejection filter, thus transfer function is written in accordance with the relation (1) of Table I; in which relations is the Laplace variable which is derived from the variable p utilized in said article (p being the reduced Laplace variable) by the relation (2) of the Table I, while the relation (3) of Table I holds true.

The other parameters of the transfer function (1) are defined in the cited reference article, such as:

ω₁ =rejection angular frequency for which the relation (4) is strictly obeyed and consequently for which the rejection is a total rejection;

Q_(o) =quality or selectivity factor indicating the steepness of the slopes of the curve |F(jω)| near ω₁ ;

ω₀ =the angular frequency associated with the poles of the transfer function. it is chosen here to have the notation ω₀ correspond to the notation ω_(p) of the cited reference book;

G=the gain of the circuit at low frequencies (when ω→0 and when s→0, the factor term of G is reduced to 1, and F(jω)→G).

The transfer function of a circuit which is no longer ideal but has a real fixed structure, for which no conditions are imposed on the value of the elements is, in the most simple case, of the second order and is expressed by the relation (5).

Here, for practical reasons of simplicity, the greatest interest is for the case in which ω₁ =ω₀ independent of the values of the filter elements, and wherein, Q₁ being the rejection factor, the relation (6) must be checked to ensure that the filter functions is a band-rejection filter, which results in one of the two relations (7) or (8).

A new parameter of the filter then becomes apparent which is the rejection R of the filter given by the relation (9) when it is assumed that ω₁ ≃ω₀.

The higher the absolute value of Q₁ (written |Q₁ |) the better is the rejection R. At its limit, the rejection R is total when |Q₁ | is infinite.

The real band-rejection filters can then be classified in two classes:

(a) the first class corresponds to the case in which Q₁ is finite, and exceeds 0 (relation (7)), whatever the elements of the filter. In these conditions, the filters cannot effect a total rejection. The limits of the filter are determined by the maximum value of Q₁. Actually, for a given value of Q₁, when the value of Q₀ increases, the rejection R decreases.

(b) the second class corresponds to the case in which the fact whether Q₁ is higher than or less than 0 depends contrary to the first class of filters, on the elements of the filter. In this case, there are specific values of the elements such that the relation (10) is satisfied, and in which the rejection R is total. The transfer function G(s) given by the relation (5) is then reduced to the function F(s) given by the relation (1).

The filters belonging to the second class have more specifically the property that they can be realized by choosing elements such as Q₁ =-Q₀ (and with ω₁ =ω₀), which results in the relation (11).

The filter then becomes of the second order all-pass type. The phase difference between the output and the input signals passes from 0 to -2π when ω varies from 0 to infinity.

The main object of the invention is to provide active filters, comprising a lowest possible number of elements so as to facilitate integration, and functioning at high and microwave frequencies.

To this effect, the integrated circuits of the filters according to the invention will advantageously be realized on gallium arsenide (GaAs).

Moreover, in accordance with the invention, one has opted for providing active band-rejection filters of the second class, which, among other advantages, renders it possible to obtain: a significant and easily controllable rejection R; a selectivity which is equally large as that of prior art passive filters described in hereafter.

The filters according to the invention can be used with advantage in frequency doublers to reject the unwanted signal at the fundamental frequency. In an all-pass filter type according to the invention, they can be used as active adjustable phase shifters at a given frequency, the phase delay being controlled by an imposed variation at ω₁.

On the other hand, band-rejection filters of the second class which operate at high frequencies are also known from the state of the art. But these circuits are realized by means of passive elements. Examples are, for example, the "Robinson bridge" circuit which is also known as a "Wien bridge", which is shown at page 121 of the reference book "Electric Filters" by T. H. Turney (Pitman and Sons, London, England, 1945). This circuit, although it is quite capable of operating at high frequencies, has several disadvantages and more specifically: a differential output, a high output impedance, and a gain which is less than unity, at low frequencies, because of the fact that it is assembled from passive elements.

The functional circuit diagram of the band-rejection circuit according to the invention is shown in FIG. 1. This circuit is formed from two portions which are bounded by broken lines in this FIG. 1: a first portion F functioning as a band-pass filter (PB), and as an amplifier; and a second portion AS which functions as an adder amplifier.

The block F has the relation (12) as its transfer function. As a result thereof, the transfer function of the overall circuit is G(s) defined by the relation (5), by using, relative to the variables defined in the foregoing, the new variables in accordance with the relations (13) and (14).

The block AS is formed by an amplifier A₁ having a gain K₁ and an amplifier A₂ having a gain K₂. The amplifier A₂ is arranged in cascade with the block F, while the amplifier A₁ is arranged in parallel with the branch formed by F and A₂. The block S₃ takes the sum of the outputs of the amplifiers A₁ and A₂, and produces the output signal V_(S) of the circuit according to the invention, whose input signal V_(E) is applied to the junction point of the input of the block F and the amplifier A₁.

In these conditions the relation (15) can be written.

By identifying the terms of the preceding relation and the terms of the relation (5), the relation (16) and G=K₁ are obtained. Consequently, the circuit according to the invention constitutes a band-rejection filter of the second class defined in the foregoing, which can realize a total rejection. It can also be highly selective, as the selectivity basically depends on the structure of the block F and not on the overall circuit of FIG. 1. It can also be used as an all-pass filter and more generally it can continuously be adjusted from band-rejection to all-pass by adjusting Q₁.

Embodiment I

This embodiment is illustrated by FIG. 2a.

For its passive portion the block F has as its equivalent circuit diagram the circuit PB shown in FIG. 2b. It is consequently equivalent to a capacitor C₁ arranged in series with a resistor R₂, a resistor R₁ being arranged between the junction of C₁ and R₂, and ground; and a capacitor C₂ being arranged between the second terminal of R₂ and ground.

In FIG. 2a, the circuit PB comprises the field-effect transistors T₁ and T₂ instead of the resistors R₁ and R₂ of the circuit diagram of FIG. 2b, and used as variable resistors controlled by the voltage source E₂.

The capacitance C₁ of the equivalent circuit diagram 2b is formed from the capacitor C₁ of the circuit of FIG. 2a. The capacitor C₂ of the equivalent circuit diagram of FIG. 2b is formed from intrinsic capacitancs of the transistors T₃ and T₄ of the circuit shown in FIG. 2a. The field-effect transistors T₃ and T₄ are arranged in parallel, their source is connected to ground. The gate of the transistor T₃ is controlled by the signal transmitted by T₂ and is biased by a voltage source E₃ via a resistor R₃.

The gate of the transistor T₄ is controlled by the same signal and is biased by the voltage source E₄ via a resistor R₄. The capacitors C₃ and C₄ shown in FIG. 2a are isolating capacitors.

The common drain of the transistors T₃ and T₄ is moreover connected to a power supply source E₁ via a load resistor R₈. The output signal V_(F) of this stage F is available at the common drains of the transistors T₃ and T₄.

This overall assembly consequently constitutes the block F of the circuit according to the invention. This assembly can be split, as regards its mode of operation, into two portions. The first portion equivalent to C₁, R₁, R₂ of the circuit of FIG. 2b is then formed from C₁, T₁, T₂ of FIG. 2a. It has no gain. The second portion equivalent to C₂ of the FIG. 2b and to the amplifier portion of the block F is formed from T₃, T₄, of FIG. 2a, and has a gain near (-G_(PB)).

According to the invention, an adjustable rejection frequency f₁ of the filter PB has been opted for. This control of the rejection frequency f₁ is obtained by an appropriate variation of the gate biasing voltage E₂ of the transistors T₁ and T₂ of the first portion. The voltage E₂ will advantageously be applied to the gates of the transistors T₁ and T₂ via a resistor of the order of magnitude of 10 kOhm, which will have for its effect to protect the transistors and to increase the rejection frequency f₁ somewhat.

On the other hand, during use of the circuit according to the invention, one may be induced to have the circuit operate at frequencies which are relatively near the cut-off frequency of the amplifier stage of the circuit F. In these circumstances, this amplifier stage produces a phase delay which brings the rejection frequency f₁ to significantly below the central frequency of the bandpass filter PB. As the gain of the transistors also varies significantly with the frequency, in the range utilized for f₁, this will render it necessary to modify the biasing of the second amplifying portion comprising T₃ and T₄ when f₁ is modified.

According to the invention, this bias control can easily be effected because of the fact that T₃ and T₄ are arranged in parallel and are biased separately by E₃ and E₄.

Biasing T₄ by E₄ via R₄ allows a coarse adjustment of the gain (-G_(PB)) of the stage F and of the rejection R.

Biasing T₃ by E₃ via R₃ allows fine adjustment of the rejection R.

To this effect, E₄ is fixed as a function of E₃. And the control of E₃ must be rather accurate. But this precision is only required in a small range.

It will also be noted that the choice of rendering f₁ adjustable is made to obtain inter alia the following two advantages:

(a) the possibility of adjusting the value of f₁ whose integrated circuits always supply widely spread values, because of the widely varying characteristics of the elements in one circuit relative to the other;

(b) the possibility to use the same circuit at several different frequencies.

Looking again at the functional circuit diagram of FIG. 1, the blocks A₁, A₂ and S₃ are represented by the block AS (amplifier-adder) bounded by the broken lines in FIG. 2a. The field-effect transistor T₅ represents the amplifier A₂ having a gain (-K₂). The field-effect transistor T₆ represents the amplifier A₁ which has a gain of (-K₁).

The transistors T₅ and T₆ are arranged in parallel, their source is connected to ground, and the output signal V_(S) is available at their common drain, which thus realizes the desired function of the adder S₃.

The transistor T₅ receives at its gate the output signal S_(F) of the amplifying portion of the stage F, that is to say the signal available on the common drain of the transistors T₃ and T₄. The transistor T₆ receives at its gate the input signal V_(E). The gate of the transistors T₅ and T₆ are moreover biased via the respective resistors R₅ and R₆, by the voltage source E₅. The common drain of the transistors T₅ and T₆ is brought to the supply voltage E₁ via the load formed by the resistors R'₇ and R₇, and by the transistor T₇ whose gate is connected to the source via the capacitor C₇.

The stage F is isolated from the stage AS by the capacitor C₅.

It will here be noted that the gain of the block F is -G_(PB), the gain of A₂ is -k₂ and the gain of A₁ is -k₁, which amounts to adding a phase shift π relative to the functional circuit diagram of FIG. 1.

On the other hand, the voltage source E₅ whose voltage is applied to the gates of the transistors T₅ and T₆ via the respective resistors R₅ and R₆, determines the gains of these transistors. Since it is not absolutely necessary to obtain a very accurate value for this voltage, the voltage source E₅ can be combined with one of the gate bias sources, for example with E₃.

The Table II shows, by way of non-limitative examples, the values of the elements for putting the circuit of FIG. 2a into effect using field-effect transistors of the normally on type having a voltage treshold of the order of:

    V.sub.T =-2.5 Volt,

and a gate length 1=0.7 μm.

The circuit obtained using the field-effect transistors having a gate width L shown in the Table II on gallium arsenide and further elements of the Table II, has given the following results:

    for E.sub.2 =0 V, f.sub.1 =3.25 GHz

    for E.sub.2 =-1.8 V, f.sub.1 =1 GHz.

Above these values, that is to say for E₂ <-1.8 V, f₁ generally decreases when E₂ decreases, but then requires a more critical adjustment.

As regards the rejection R, when the value of the voltage source E₃ is controlled with a precision of ±25 mV, the rejection R always is:

    R=50 dB at f.sub.1 =3.25 GHz

    and R≧48 dB at f.sub.1 =1 GHz.

It will be noted that at f₁ =1 GHz, the value of the rejection R is lower as the transistor T₃ participates more in the gain of the amplifier of the circuit F.

As regards the gain obtained by the circuit, this gain is:

    G=10 dB.

Biasing the amplifier stage of F was such that: f₁ =3.25 GHz was obtained for E₄ =-0.85 V and E₃ =-0.815 V and f₁ =1 GHz was obtained for E₄ =-1.7 V and E₃ =-0.830 V.

Finally, by way of example, the amplitude response of the filter of FIG. 2a as a function of the frequency f is represented by the curve of FIG. 2c, which is obtained by computer simulation; and the curve of the phase shift φ, which was also obtained by computer simulation, between the output signal V_(s) and the input signal V_(E) as a function of the frequency f is shown in FIG. 2d.

Reverting to the equation (16) which applies, as has been described in the foregoing, to the present circuit, it has already been remarked hereinbefore that:

(a) the filter circuit according to the invention is of the band-rejection type when the relation (6) is satisfied. The structure according to the invention renders it possible to obtain a positive or a negative value for Q₁ and to satisfy relation (10).

(b) the circuit according to the invention also renders it possible to obtain

    Q.sub.1 =-Q.sub.0,

which corresponds to the case in which the circuit has the all-pass function. The circuit according to the invention renders it possible to pass from the band-rejection function to the all-pass function using the same elements.

It is actually sufficient to have the bias of the gates of the transistors of the different stages vary, to obtain the variation

either of k₁,

either of k₂,

either of G_(PB).

It is then possible to change in a continuous manner from:

    Q.sub.1 =-∞ (band-rejection) to Q.sub.1 =-Q.sub.0 (all-pass).

                  TABLE I                                                          ______________________________________                                          ##STR1##                                                                      P = s/ω.sub.1 (2)                                                        S = jω (3)                                                               F(jw.sub.1) = 0 (4)                                                             ##STR2##                                                                      |Q.sub.1 | > Q.sub.o (6)                                     Q.sub.1 > Q.sub.o (7)                                                          Q.sub.1 < -Q.sub.o (8)                                                          ##STR3##                                                                      1/Q.sub.1 = 0 (10)                                                             |G(jω)| = G = constant (11)                             ##STR4##                                                                      ω.sub.1 = ω.sub.o = ω.sub.PB (13)                            Q.sub.0 = Q.sub.PB (14)                                                        V.sub.s /V.sub.E = H(s) · k.sub.2 + k.sub.1                            ##STR5##                                                                       ##STR6##                                                                      ______________________________________                                    

                  TABLE II                                                         ______________________________________                                         CAPACITORS          Transistors                                                (pF)      Resistors (k)                                                                            L (μm) Voltage                                          ______________________________________                                         C.sub.1                                                                              0,2     R.sub.3                                                                               20   T.sub.1                                                                             10   E.sub.1                                                                             6                                     C.sub.3                                                                              0,5     R.sub.4                                                                               20   T.sub.2                                                                             10   E.sub.2                                                                             0 → -1,8                       C.sub.4                                                                              0,5     R.sub.5                                                                               10   T.sub.3                                                                             20   E.sub.3                                                                             ≃ -0,8                  C.sub.5                                                                              1,0     R.sub.6                                                                               10   T.sub.4                                                                             20   E.sub.4                                                                             -0,85 → -1,7                   C.sub.6                                                                              1,0     R.sub.8                                                                               0,6  T.sub.7                                                                             20                                              C.sub.7                                                                              1,0     R.sub.7                                                                               10   T.sub.5                                                                             20   E.sub.5                                                                             -0,8                                                R.sub.7                                                                               14   T.sub.6                                                                             20                                              ______________________________________                                     

What is claimed is:
 1. An active filter circuit operable in a band-rejection mode and in an all-pass mode, comprising:a filter and amplifier circuit comprising filtering means comprised of an RC filter circuit for filtering an input signal applied thereto, said filtering means having a transfer function which is of the first order in the numerator and of the second order in the denominator and amplifying means for amplifying the output of said filtering means; an amplifier circuit for amplifying the input signal applied to said filter and amplifier circuit; a second amplifier circuit for amplifying the output of said filter and amplifier circuit; and summing means for summing the respective output signals of said first and second amplifier circuits; whereby the active filter circuit has a transfer function which is of the second order in the numerator and second order in the denominator and the active filter mode can be changed between a band-rejection mode and an all-pass mode by changing the RC component values and amplifying means and amplifier gains.
 2. A circuit as claimed in claim 1, characterized in that the filter-amplifier block F is an active circuit containing a block functioning as an amplifier and a block PB functioning as a second-order bandpass.
 3. A circuit as claimed in claim 2, characterized in that the circuit F is equivalent, as regards its passive portion PB to a filter constituted by a capacitor C₁ and a resistor R₂ arranged in series between its input E and its output S_(F), a resistor R₁ positioned between the junction point of the capacitor C₁ and the resistor R₂, and a capacitor C₂ positioned between the output S_(F) and ground.
 4. A circuit as claimed in claim 3, characterized in that in the circuit F the resistances R₁ and R₂ are constituted by the respective field-effect transistors T₁ and T₂, the source of the transistor T₁ being connected to ground, its drain being connected to the source of the transistor T₂ and to the terminal of the capacitor C₁ opposite the input E, and the grids of the transistors T₁ and T₂ being biased by a controllable D.C. voltage source E₂ to have the value of the resistors R₁ and R₂ and the frequency f₁ of the rejection of the filter vary, and in that the capacitor C₂ is constituted by intrinsic capacitances of the field-effect transistors T₃ and T₄ of an amplifier stage formed by two parallel-arranged transistors T₃ and T₄, their common source is connected to ground, their common drain to a D.C. supply voltage source E₁ via a load resistor R₈, the grids of the transistors T₃ and T₄ being controlled by the signal available at the drain of the processor T₂ via the respective capacitors C₃ and C₄, and these grids being in addition biased by the controllable D.C. voltage sources, E₃ via a resistor R₃ for the processor T₃ and E₄ via a resistor R₄ for the transistor T₄, respectively, the value of the D.C. voltage E₃ being chosen for a fine adjustment of the rejection value R of the filter, and the value of the D.C. voltage E₄ being chosen for a coarse adjustment of the gain (-G_(PB) ) of the amplifier stage and the rejection R, the output signal V_(PB) of the circuit F being available at the junction S_(F) of the drains of the transistors T₃ and T₄.
 5. A circuit as claimed in claim 4, characterized in that the amplifier block A₂ is constituted by a field-effect transistor T₅ whose source is connected to ground, the drain to the output S, and whose grid receives the signal V_(PB) from the output of the block F via a capacitor C₅, the drain of this transistor T₅ being moreover brought to the supply voltage E₁ via the load resistor R₉ and the grid of this transistor T₅ being biased via a resistor R₅ by a controllable D.C. voltage source E₅ to have the gain (-k₂) of this amplifier block vary, and in that the amplifier block A₁ is formed by a field-effect transistor T₆ which is arranged in parallel with the transistor T₅ to effect the addition S₃, the grid of the transistor T₆ receiving the input signal V_(E) of the circuit via a capacitor C₆ and being in addition biased via a resistor R₆ by the voltage source E₅ to have the gain (-k₁) of this amplifier block vary.
 6. A circuit as claimed in claim 5, characterized in that the load resistance R₉ of the transistors T₅ and T₆ is an active load constituted by a field-eefect transistor T₇ whose source is connected to the common drains of the transistors T₅ and T₆, and whose drain is brought to the D.C. supply voltage E₁, the bias of the grid of the transistor T₇ being realized by connecting it to the centre tap of a divider bridge formed by the resistors R₇ and R'₇ arranged between ground and the voltage E₁, and the grid being moreover connect to the source of T₇ via a capacitor C₇, and in that the load resistance R₈ of the transistors T₃ and T₄ is a resistor.
 7. A circuit as claimed in anyone of the claims 5 or 6, characterized in that it has the function of a band-rejection filter for controlling the values of the voltages E₁, E₂, E₃, E₄, E₅, one iwht respect to the others to obtain the gains k₁, k₂, G_(PB) of the amplifier blocks in such a manner that the band-rejection R of this circuit is higher than
 1. 8. A circuit as claimed in anyone of the claims 5 or 6, characterized in that it has the function of an all-pass for controlling the values of the voltages E₁, E₂, E₃, E₄, E₅ one with respect to the others to obtain the gains k₁, k₂, G_(PB) of the amplifier blocks in such a manner that the rejection factor Q₁ is opposed to the quality factor Q₀.
 9. A circuit as claimed in anyone of the claims 5 or 6, characterized in that, for controlling the values of the voltages E₃ and E₄ with respect to the voltages E₁, E₂, E₅, to obtain the gain variations k₁, k₂, and G_(PB) a continuous variation of the rejection factor Q₁ between -∞ and +∞ is obtained.
 10. A circuit as claimed in anyone of the claims 4, 5 or 6 characterized in that it is integrated on a gallium-arsenide (GaAs) substrate and is obtained using field-effect transistors of a type which is normally conductive in the absence of a bias.
 11. A circuit as claimed in claim 7, characterized in that it is integrated on a gallium-arsenide (GaAs) substrate and is obtained using field-effect transistors of a type which is normally conductive in the absence of a bias.
 12. A circuit as claimed in claim 8, characterized in that it is integrated on a gallium-arsenide (GaAs) substrate and is obtained using field-effect transistors of a type which is normally conductive in the absence of a bias.
 13. A circuit as claimed in claim 9, characterized in that it is integrated on a gallium-arsenide (GaAs) substrate and is obtained using field-effect transistors of a type which is normally conductive in the absence of a bias. 